Subgroups — C₂×#15688974 #20245722

Order 6016.

928 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
2	C₂²×C₄×Dic₄₇	C₂	1	2	yes	maximal
3	C₂²×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#15688974	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₄₇	C₂²	1	2	yes	—
8	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₇⋊C₄	C₄	1	16	yes	complemented
11	C₂×Dic₄₇⋊C₄	C₂²	1	8	yes	—
12	C₂×C₄×Dic₄₇	—	2	8	no	—
13	C₂×C₄×Dic₄₇	C₄	1	8	yes	complemented
14	C₂×C₄×Dic₄₇	C₂²	1	8	yes	—
15	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
16	C₄₇⋊#95	C₂²	1	4	yes	—
17	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
19	#95×C₄₇	C₂²	1	4	yes	—
20	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	—	2	4	no	—
22	C₂²×C₄×C₄₇	—	2	4	no	—
23	C₂²×C₄×C₄₇	—	2	4	no	—
24	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂×C₄	1	8	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
27	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
28	C₂²×Dic₄₇	—	2	4	no	—
29	C₂²×Dic₄₇	—	2	4	no	—
30	C₂²×Dic₄₇	C₂×C₄	1	8	yes	—
31	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
32	C₂²×Dic₄₇	C₂×C₄	1	8	yes	—
33	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
34	C₂²×Dic₄₇	D₄	1	4	yes	—
35	C₂²×Dic₄₇	Q₈	1	4	yes	—
36	C₂²×Dic₄₇	C₂³	1	4	yes	—
37	C₂²×Dic₄₇	C₂³	1	2	yes	—
38	C₂²×Dic₄₇	C₂³	1	2	yes	—
39	Dic₄₇⋊C₄	C₂×C₄	1	32	yes	complemented
40	C₄×Dic₄₇	—	2	16	no	—
41	C₄×Dic₄₇	C₂×C₄	1	16	yes	complemented
42	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
43	C₂³×C₄₇	C₂²×C₄	1	4	yes	—
44	C₂³×C₄₇	C₂×D₄	1	2	yes	—
45	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
46	C₂³×C₄₇	#41	1	4	yes	—
47	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
48	C₂×C₄×C₄₇	—	2	8	no	—
49	C₂×C₄×C₄₇	—	2	16	no	—
50	C₂×C₄×C₄₇	—	2	4	no	—
51	C₂×C₄×C₄₇	—	2	4	no	—
52	C₂×C₄×C₄₇	—	2	4	no	—
53	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
54	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
55	C₂×Dic₄₇	—	2	16	no	—
56	C₂×Dic₄₇	—	2	4	no	—
57	C₂×Dic₄₇	—	2	4	no	—
58	C₂×Dic₄₇	C₄²	1	16	yes	complemented
59	C₂×Dic₄₇	C₄⋊C₄	1	16	yes	complemented
60	C₂×Dic₄₇	C₂²×C₄	1	8	yes	—
61	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
62	C₂×Dic₄₇	C₂²×C₄	1	8	yes	—
63	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
64	C₂×Dic₄₇	C₂×D₄	1	4	yes	—
65	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
66	C₂²×C₄₇	C₂×C₄²	1	4	yes	—
67	C₂²×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
68	C₂²×C₄₇	#117	1	4	yes	—
69	C₂²×C₄₇	C₄×D₄	1	8	yes	—
70	C₂²×C₄₇	C₄×Q₈	1	8	yes	—
71	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
72	C₂²×C₄₇	C₂³×C₄	1	2	yes	—
73	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
74	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
75	C₂²×C₄₇	C₂×#41	1	2	yes	—
76	C₄×C₄₇	—	2	4	no	—
77	C₄×C₄₇	—	2	8	no	—
78	Dic₄₇	—	2	8	no	—
79	Dic₄₇	C₂×C₄²	1	8	yes	complemented
80	Dic₄₇	C₂×C₄⋊C₄	1	8	yes	complemented
81	C₂×C₄×C₄⋊C₄	—	47	1	no	maximal, Sylow
82	C₂×C₄₇	C₄×C₄⋊C₄	1	8	yes	complemented
83	C₂×C₄₇	C₂²×C₄²	1	1	yes	characteristic
84	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄₇	C₂×#117	1	1	yes	characteristic
86	C₂×C₄₇	C₂×C₄×D₄	1	2	yes	—
87	C₂×C₄₇	C₂×C₄×Q₈	1	2	yes	—
88	C₂²×C₄⋊C₄	—	47	2	no	—
89	C₂²×C₄²	—	47	1	no	—
90	C₂²×C₄²	—	47	2	no	—
91	C₄×C₄⋊C₄	—	47	8	no	—
92	C₂×#95	—	47	1	no	—
93	C₂×#95	D₄₇	1	1	yes	characteristic
94	C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
95	C₂³×C₄	—	47	1	no	—
96	C₂³×C₄	—	47	1	no	—
97	C₂³×C₄	—	47	2	no	—
98	C₂³×C₄	C₂×D₄₇	1	2	yes	—
99	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
100	C₂×C₄⋊C₄	—	47	16	no	—
101	C₂×C₄⋊C₄	—	47	8	no	—
102	C₂×C₄²	—	47	8	no	—
103	C₂×C₄²	—	47	4	no	—
104	C₂×C₄²	—	47	8	no	—
105	C₂×C₄²	—	94	8	no	—
106	#95	—	47	4	no	—
107	#95	C₂×D₄₇	1	4	yes	—
108	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
109	C₂²×C₄	—	2	4	no	—
110	C₂²×C₄	—	2	4	no	—
111	C₂²×C₄	—	2	4	no	—
112	C₂²×C₄	—	47	4	no	—
113	C₂²×C₄	—	47	4	no	—
114	C₂²×C₄	—	47	8	no	—
115	C₂²×C₄	—	47	4	no	—
116	C₂²×C₄	—	47	4	no	—
117	C₂²×C₄	—	47	2	no	—
118	C₂²×C₄	—	47	2	no	—
119	C₂²×C₄	—	47	8	no	—
120	C₂²×C₄	—	47	4	no	—
121	C₂²×C₄	—	94	4	no	—
122	C₂²×C₄	—	94	4	no	—
123	C₂²×C₄	C₄×D₄₇	1	4	yes	—
124	C₂²×C₄	C₄×D₄₇	1	8	yes	—
125	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
126	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
127	C₄⋊C₄	—	47	32	no	—
128	C₄²	—	47	16	no	—
129	C₄²	—	94	16	no	—
130	C₂³	C₂×C₄×D₄₇	1	2	yes	—
131	C₂³	C₂×C₄×D₄₇	1	4	yes	—
132	C₂³	D₄×D₄₇	1	2	yes	—
133	C₂³	#10625352	1	4	yes	—
134	C₂³	Q₈×D₄₇	1	2	yes	—
135	C₂³	C₂³×D₄₇	1	1	yes	characteristic
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	16	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	47	16	no	—
142	C₂×C₄	—	47	16	no	—
143	C₂×C₄	—	47	4	no	—
144	C₂×C₄	—	47	4	no	—
145	C₂×C₄	—	47	8	no	—
146	C₂×C₄	—	47	4	no	—
147	C₂×C₄	—	47	4	no	—
148	C₂×C₄	—	47	8	no	—
149	C₂×C₄	—	94	16	no	—
150	C₂×C₄	—	94	4	no	—
151	C₂×C₄	—	94	4	no	—
152	C₂×C₄	C₂×C₄×D₄₇	1	4	yes	—
153	C₂×C₄	C₂×C₄×D₄₇	1	8	yes	—
154	C₂²	C₄²×D₄₇	1	4	yes	—
155	C₂²	C₄⋊C₄×D₄₇	1	4	yes	—
156	C₂²	#13093980	1	4	yes	—
157	C₂²	(C₂²⋊D₄₇)⋊C₄	1	8	yes	—
158	C₂²	#13093989	1	8	yes	—
159	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
160	C₂²	C₂²×C₄×D₄₇	1	2	yes	—
161	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
162	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
163	C₂²	C₂×#10625352	1	2	yes	—
164	C₄	—	2	4	no	—
165	C₄	—	2	8	no	—
166	C₄	—	47	8	no	—
167	C₄	—	47	8	no	—
168	C₄	—	94	8	no	—
169	C₂	#15688974	1	8	yes	direct product factor
170	C₂	C₂×C₄²×D₄₇	1	1	yes	characteristic
171	C₂	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
172	C₂	C₂×#13093980	1	1	yes	characteristic
173	C₂	C₂×(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
174	C₂	C₂×#13093989	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂×C₄₇	C₂²×C₄²
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	C₂×C₄×C₄⋊C₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #15688974	C₂	direct (N × H)
10. C₂×Dic₄₇⋊C₄	C₄	semidirect
13. C₂×C₄×Dic₄₇	C₄	semidirect
39. Dic₄₇⋊C₄	C₂×C₄	semidirect
41. C₄×Dic₄₇	C₂×C₄	semidirect
58. C₂×Dic₄₇	C₄²	semidirect
59. C₂×Dic₄₇	C₄⋊C₄	semidirect
79. Dic₄₇	C₂×C₄²	semidirect
80. Dic₄₇	C₂×C₄⋊C₄	semidirect
82. C₂×C₄₇	C₄×C₄⋊C₄	semidirect
94. C₄₇	C₂×C₄×C₄⋊C₄	semidirect
169. C₂	#15688974	direct (N × H)

Subgroups — C2×#15688974 #20245722

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688974 #20245722